Equivalent method for near field, mask 3D near field correction method, storage medium

Abstract

The application discloses a near-field equivalent method, a mask 3D near-field correction method and a storage medium. The optical near-field equivalent method comprises the following steps: setting a three-axis coordinate system, so that the initial propagation direction of a light source with a preset angle is propagated along a first axis, and an initial wave vector and a polarization direction are obtained; performing a rotation operation on the initial wave vector and the polarization direction according to the preset angle of the light source; analyzing the polarization direction and the polarization vector of the light source after the rotation operation; rotating the polygon and the light source according to the preset angle of the polygon, so that a new wave vector and a corresponding rotation angle are obtained; analyzing the polarization direction, the polarization vector and the component of the light source after the second rotation operation; generating an edge near-field under equivalent conditions by using a 2D strict electromagnetism algorithm; and performing linear superposition according to the respective components based on the polarization direction of the light source after the second rotation operation, so that an equivalent near-field result is obtained. The application reduces the calculation burden of near-field generation.

Description

Technical Field

[0001] This invention relates to the technical field of photolithography technology in semiconductor manufacturing, and more particularly to an equivalent method for calculating the accurate near field and the near field during imaging while taking into account the thick mask effect. Background Technology

[0002] In the manufacturing process of integrated circuits (ICs), to obtain the target pattern on the wafer, it is necessary to transfer the pattern from a photomask to the surface of the silicon wafer, a process known as photolithography. Photolithography typically involves exposure, development, and subsequent etching steps. During exposure, light emitted from a light source passes through the transparent areas of the photomask and illuminates the silicon wafer coated with photoresist. The areas of the photoresist not blocked by the photomask undergo a chemical reaction upon exposure to light. In the development step, the different solubility of the developer in the photoresist and the unphotoresisted areas are used to form a photolithographic pattern, transferring the pattern from the photomask to the photoresist. In the etching step, the silicon wafer is etched based on the photolithographic pattern formed by the photoresist layer, further transferring the pattern from the photomask onto the silicon wafer.

[0003] As Moore's Law advances and design dimensions continue to shrink, the minimum size of the design pattern approaches the limits of photolithography imaging systems. The diffraction effect of light becomes increasingly pronounced, resulting in severe distortion of the image obtained from exposure compared to the pattern on the photomask. Consequently, the actual pattern formed on the silicon wafer through photolithography differs from the design pattern. This phenomenon is known as the Optical Proximity Effect (OPE). To correct the OPE, Optical Proximity Correction (OPC) was developed. This correction adjusts the pattern on the photomask to offset the OPE, achieving a photolithography result that better matches the desired outcome.

[0004] To perform optical proximity correction, accurate calculation of lithographic imaging results is first required. Traditional lithographic imaging calculation methods use a thin mask approximation, assuming the mask thickness is infinitely thin. In this case, the distribution of the diffracted light field can be calculated using the Huygens–Fresnel principle and the Fresnel-Kirchoff diffraction formula. In practical applications, the Hopkins model is typically used to change the imaging calculation process. By first calculating the cross-transmission matrix (TCC) of the light source and lens group pupils, and then calculating the effect of the TCC and the thin mask, the calculation speed for solving the spatial image is greatly improved.

[0005] As the size of lithographic patterns continues to shrink, the errors introduced by thin mask approximations have become non-negligible. It is necessary to consider the impact of scattering effects from real masks of a certain thickness on imaging. Rigorous computational electromagnetic methods, such as the Finite-Difference Time-Domain (FDTD) and Rigorous Coupled-Wave Method (RCWA), can accurately solve for the near-field near the mask. However, due to their high computational cost, these rigorous methods cannot be applied to lithographic imaging calculations. Therefore, a method that balances computational efficiency and the accuracy of rigorous methods is needed, employing a traditional method that corrects the near-field obtained using line / space patterns obtained under rigorous methods. To meet this application requirement, a fast and efficient method is needed to generate the near-field generated when light sources from different directions illuminate edges in different directions.

[0006] Traditional photolithography thin mask approximations are gradually failing to meet the accuracy requirements of imaging results in photolithography imaging calculations at nodes of 14nm and below. While rigorous electromagnetic methods capable of accurately solving the effect of mask thickness on the near-field diffraction suffer from enormous computational overhead due to 3D mesh generation and iterative calculation methods, the need to comprehensively consider various scenarios, especially considering multi-angle illumination determined by the light source shape and the possible angular directions of polygon edges, further complicates the computational burden. Summary of the Invention

[0007] To address the problem of excessive computational overhead in generating near fields in existing technologies, this invention proposes an equivalent method for near fields, a method for correcting 3D near fields using masks, and a storage medium.

[0008] The equivalent method for optical near-field proposed in this invention includes:

[0009] Step 1: Set up a three-axis coordinate system so that the initial propagation direction of the light source at the preset angle propagates along the first axis, and obtain the initial wave vector and polarization direction.

[0010] Step 2: Rotate the initial wave vector and polarization direction once along the second axial direction and once along the third axial direction according to the preset angle of the light source.

[0011] Step 3: Analyze the polarization direction and polarization vector of the light source after the rotation operation;

[0012] Step 4: Rotate the polygon and the light source according to the preset angle of the polygon so that the angle of the polygon becomes 0 degrees and the direction of the light source relative to the edge of the polygon remains unchanged.

[0013] Step 5: Obtain the new wave vector and the corresponding rotation angle;

[0014] Step 6: Analyze the polarization direction, polarization vector, and composition of the light source after the second rotation operation based on the rotation angle obtained in Step 5.

[0015] Step 7: Decompose the polarization vector into its corresponding polarization direction to obtain the components in each polarization direction;

[0016] Step 8: Generate the edge near field under equivalent conditions using a 2D rigorous electromagnetic algorithm;

[0017] Step 9: Based on the polarization direction of the light source after the second rotation operation, linearly superimpose the corresponding components to obtain the equivalent near-field results of the light source at the preset angle and the polygon at the preset angle.

[0018] Furthermore, the three-axis coordinate system is an xyz-axis coordinate system.

[0019] Furthermore, when the first axial direction is the x-axis, the second axial direction is the y-axis, and the third axial direction is the z-axis, the polarization direction along the y-axis in step 3 is Ey = (-sinβ, cosβ, 0), the polarization direction along the z-axis is Ez = (sinαcosβ, sinαsinβ, cosα), and the polarization vector is P = p·dEy + q·dEz, where α and β are preset angles of the light source, p is the initial component of the polarization direction along the y-axis, and q is the initial component of the polarization direction along the z-axis.

[0020] Furthermore, in step 6, the polarization direction along the y-axis after the light source undergoes a second rotation is Ey2 = (-sinβ2, cosβ2, 0), and the polarization direction along the z-axis is Ez2 = (sinα2cosβ2, sinα2sinβ2, cosα2), with the polarization vector being...

[0021] Furthermore, in step 7, the components of the polarization vector P2 along the polarization direction Ey2 are: The components of the polarization vector in the polarization direction Ez2 are:

[0022] The mask 3D near-field correction method proposed in this invention adopts the equivalent near-field method described in the above technical solution.

[0023] The computer storage medium proposed in this invention is used to store a computer program, which executes the near-field equivalent method described in the above technical solution when it runs.

[0024] Compared with the prior art, the present invention has the following beneficial effects.

[0025] 1. Capable of handling various custom light source directions and calculating free-form light sources. Current mainstream 3D thick-mask lithography imaging models, limited by computational overhead, cannot complete the simulation of all sampling points (201*201, each with different light intensity and direction, specified by the semiconductor chip manufacturing manufacturer) for all light source directions within a limited time. A common approach is to select only 4 sampling points and replace all others. This results in significant errors when the light source shape has poor symmetry. The method provided in this patent, however, significantly improves computational speed, enabling calculation of sampling points for all light source directions within a predetermined time, thus achieving the calculation of free-form light sources.

[0026] 2. It can handle polygon edges in different directions, and can convert edges in each direction into Manhattan polygons with equivalent lighting conditions to complete the calculation.

[0027] 3. While covering a variety of complex conditions, this invention also ensures that complex 3D situations can be reduced to 2D for rigorous electromagnetic simulation, which is about 1000 times faster than 3D simulation with the same accuracy. Attached Figure Description

[0028] The present invention will now be described in detail with reference to the embodiments and accompanying drawings, wherein:

[0029] Figure 1 This is a flowchart of an embodiment of the present invention.

[0030] Figure 2 It is the near-field total field obtained using existing technology.

[0031] Figure 3 It is the near-field total field in the Ey polarization direction obtained by utilizing the equivalent incident tilt of the present invention.

[0032] Figure 4 It is the near-field total field in the Ez polarization direction obtained by utilizing the equivalent incident tilt of the present invention.

[0033] Figure 5 It is along Figure 2 The near-field edge field is obtained by drawing the diagonal lines in the diagram.

[0034] Figure 6 It is along Figure 3 The near-field edge field obtained by drawing the horizontal line in the figure.

[0035] Figure 7 It is along Figure 4 The near-field edge field obtained by drawing the horizontal line in the figure.

[0036] Figure 8 yes Figure 6 , Figure 7The near-field edge field obtained by superimposing two polarization directions.

[0037] Figure 9 This is a comparison diagram of the near-field edge field obtained by existing technology and the near-field edge field obtained by this invention. Detailed Implementation

[0038] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0039] Therefore, a feature pointed out in this specification is used to describe one feature of one embodiment of the invention, and does not imply that every embodiment of the invention must have the described feature. Furthermore, it should be noted that this specification describes many features. Although certain features may be combined to illustrate possible system designs, these features may also be used in other combinations not explicitly stated. Therefore, unless otherwise stated, the described combinations are not intended to be limiting.

[0040] The equivalent method for optical near-field of the present invention includes the following steps.

[0041] Step 1: Establish a three-axis coordinate system such that the initial propagation direction of the light source at the preset angle propagates along the first axis, and obtain the initial wave vector and polarization direction. In one embodiment, the three-axis coordinate system is specifically an xyz coordinate system, where the first axis can be any one of the x-axis, y-axis, or z-axis.

[0042] Taking the x-axis as the initial propagation direction of the light source as an example, where the x-axis is defined as the axis perpendicular to the plane of the layout, the light source is set above the layout, and the polygon is a polygon with a hypotenuse, that is, the polygon has a side in the plane of the layout that is not parallel to the y-axis or z-axis. Assume that the deflection angle of the hypotenuse of the polygon is δ, and the angle of a sampling point of the light source is α or β.

[0043] At this time, the direction of the wave vector The coordinates are (1, 0, 0). At this point, the polarization direction of the light lies in the yz plane. The polarization directions Ey (along the y-axis) and Ez (along the z-axis) are defined as the two "fundamental directions" of the electric field polarization of this light wave. Any other polarization direction can be obtained by the linear superposition of the polarization directions Ey and Ez. The components of the polarization directions Ey and Ez are p and q, respectively, where p is the initial component along the y-axis and q is the initial component along the z-axis, both being known light source parameters.

[0044] The rotation matrices along the x, y, and z axes are defined as follows.

[0045]

[0046]

[0047] Step 2: Rotate the initial wave vector and polarization direction once along the second axis and once along the third axis, respectively, according to the preset angle of the light source.

[0048] α and β are the angles of a sampling point of an arbitrarily chosen light source, and are also known light source parameters. In practical applications, the foundry (semiconductor chip manufacturing manufacturer) provides a 201*201 table, i.e., 201*201 sampling points, each sampling point representing a direction and having an intensity value. This invention can calculate for all non-zero light source directions.

[0049] First, rotate the light source by an angle α along the y-axis, and then rotate it by β along the z-axis. The direction of the rotated wave vector k is: (cosαcosβ, cosαsinβ, -sinα).

[0050] Step 3: Analyze the polarization direction and polarization vector of the light source after the rotation operation.

[0051] The initial polarization directions Ey and Ez are also rotated by corresponding angles from (0, 1, 0) and (0, 0, 1) respectively, resulting in the following new polarization directions:

[0052] Ey=R z (β)·R y (α)·(0,1,0)=(-sinβ,cosβ,0);

[0053] Ez = R z (β)·R y (α)·(0,0,1)=(sinαcosβ, sinαsinβ, cosα).

[0054] The components for each polarization direction remain p and q. The purpose of defining this rotation angle is to facilitate the handling of polarization directions and ensure that the polarization direction is always perpendicular to the wave vector direction. This rotation angle definition is a common method in FDTD simulations. The method of ensuring the polarization direction is perpendicular to the wave vector direction is based on the following principle: the initial wave vector direction and polarization direction are along x, y, and z respectively, ensuring perpendicularity; then, performing the same rotation (multiplying by the same rotation matrix) on the three directions still results in mutual perpendicularity. At this point, the polarization vector is:

[0055] P = p·dEy + q·dEz.

[0056] In this formula, α and β are angles taken from the sample of the given light source, p is the initial component along the polarization direction of the y-axis, and q is the initial component along the polarization direction of the z-axis.

[0057] Step 4: Rotate the polygon and the light source according to the preset angle of the polygon, so that the angle of the polygon becomes 0 degrees, and the direction of the light source relative to the edge of the polygon remains unchanged.

[0058] Assuming the preset angle of the polygon is δ, perform a rotation of angle -δ along the x-axis on the entire system (i.e., the polygon and the light source), so that the angle of the polygon becomes 0 degrees, and the direction of the light source relative to the edge of the polygon remains unchanged.

[0059] Step 5: Obtain the new wave vector and the corresponding rotation angle.

[0060] At this time, the new wave vector Direction is

[0061] That is, (cosαcosβ, cosαsinβcosδ+sinαsinδ, cosαsinβsinδ-)

[0062] sinαcosδ).

[0063] The new wave vector k2 is also decomposed into two rotations along the y-axis and z-axis sequentially. The angles of the two rotations are calculated as follows:

[0064]

[0065]

[0066] From the above formula, we can obtain:

[0067] α2=-sin -1 (cosαsinβsinδ-sinαcosδ);

[0068] β2=sin -1 [(cosαsinβcosδ+sinαsinδ)÷cosα2].

[0069] That is, when the edges of the polygon are visited in a Manhattan configuration, light sources rotated sequentially along the y-axis and z-axis by α2 and β2 respectively can generate the same near field as when the edges are rotated by α and β and then by δ. The polarization vector after the equivalent rotation is:

[0070]

[0071] Figure 2This demonstrates the near-field total field generated through rigorous electromagnetic 3D simulation, showing a light source with oblique incidence and polygonal deflection. Figure 2 The mask material used was 70 nm thick MoSi with a refractive index n = 2.26. The experimental objective was to calculate the deflection angle δ = 30° of the polygon; the incident light source was incident at tilted angles α and β of 15° and 10°, respectively. Figure 5 Indicates along Figure 2 The waveform diagram of the near field of the region along the perpendicular direction of the edge, extracted by the diagonal line drawn in the middle. Figure 2 and Figure 5 It is the total incoming field and the corresponding waveform obtained using existing technology.

[0072] Figure 3 , Figure 4 This demonstrates the total incident field in different polarization directions, generated through rigorous electromagnetic 3D simulation with a light source incident at an angle and without polygonal deflection. The mask materials used in the two diagrams are... Figure 2 They are the same, the difference being that polygons do not have a deflection angle, meaning the deflection angle of a polygon is 0. At the same time... Figure 3 The total near-field field of Ey polarization is shown based on the equivalent deflection angles α2 and β2 using the above steps of the present invention. Figure 4 The Ez-polarized near-field total field is shown based on the equivalent deflection angles α2 and β2 using the steps described above in this invention. However... Figure 3 , Figure 4 Instead of using the dimension reduction calculation (2D electromagnetic calculation) of this invention, the same 3D electromagnetic algorithm is used to verify the near-field results of the equivalent deflection angle of this invention. Step 6: Analyze the polarization direction, polarization vector, and composition of the light source after the second rotation operation based on the rotation angle in step 5.

[0073] Analyze the polarization direction, polarization vector, and composition of the light source after the second rotation operation.

[0074] After calculation, the new polarization direction is determined from the equivalent perspective of the Manhattan polygon as follows:

[0075]

[0076] Ez2=(sinα2cosβ2, sinα2sinβ2, cosα2).

[0077] Step 7: Decompose the polarization vector into the corresponding polarization direction to obtain the components in each polarization direction.

[0078]

[0079]

[0080] Step 8: Generate the edge near field under equivalent conditions using a 2D rigorous electromagnetic algorithm.

[0081] In the 2D case, periodic boundary conditions are set along the z-direction of the edge, and the solution is obtained only in the xy-plane.

[0082] Here, the x-direction is the direction of light propagation (without deflection), which is also perpendicular to the mask. The z-direction is the direction of the simulated edge, and the y-direction is the direction on the mask plane that is perpendicular to the edge.

[0083] The premise for setting periodic boundary conditions along the z-direction of an edge is that the simulated structure has periodic repetition along the z-direction. In most simulation cases, the simulated edge can be considered to be sufficiently long compared to the width, approximately infinitely long, and therefore the direction along the edge is infinitely repetitive.

[0084] Projecting the wave vector and polarization from 3D onto the xy plane avoids redundant calculations only in the z-direction. The calculation results are consistent along the z-axis, so the calculation is only performed once. This projection does not ignore the wave vector and polarization direction present in the z-direction and does not introduce any bias into the results.

[0085] The light source needs to be set up according to the deflection angles α2 and β2 obtained in steps 4 and 5 above, and then solved separately in the polarization directions Ey and Ez.

[0086] Figure 6 , Figure 7 These represent the near-field distributions of the Ey and Ez deflection components along the perpendicular direction of the mask edge, calculated using the 2D electromagnetic algorithm at deflection angles α2 and β2, respectively, after dimensionality reduction to 2D in step 8. Figure 6 Indicates along Figure 3 The waveform diagram of the near field of the region along the vertical direction of the edge extracted by the horizontal line drawn in the middle. Figure 7 Indicates along Figure 4 The waveform diagram of the near field of the region along the vertical direction of the edge extracted by the horizontal line drawn in the middle.

[0087] Step 9: Based on the polarization direction of the light source after the second rotation operation, linearly superimpose the corresponding components to obtain the equivalent near-field results of the light source at the preset angle and the polygon at the preset angle.

[0088] Figure 8 This represents the polarization component calculated in step 7, and the result obtained by superimposing the diffraction near fields of the two equivalent light sources calculated in step 8 according to the components. Figure 9 express Figure 5 The results shown are consistent with Figure 8 The results are compared, where the dashed lines represent... Figure 8 The results shown are represented by solid lines. Figure 5The results shown can be compared to those of the 3D electromagnetic algorithm. Although the 2D electromagnetic algorithm significantly reduces the computational load, the near-field results obtained by the method of this invention are still similar to those obtained by the 3D electromagnetic algorithm. The two are equivalent near-field results.

[0089] This invention, through the aforementioned technical solution, addresses the near-field calculation of polygons with hypotenuses under corresponding light sources, which previously required 3D simulation calculations. Instead, it employs a method of straightening the polygon and simultaneously superimposing two new light sources to simulate the near-field of a hypotenuse polygon under any angle of light. This reduces the calculation to a 2D electromagnetic algorithm, significantly lowering computational complexity. Consequently, it enables the calculation of the near-field of polygons with arbitrary angles and deflections, avoiding the biases inherent in existing technologies that rely solely on a few sampling points due to the difficulty of 3D simulation calculations.

[0090] This invention, through the aforementioned technical solution, provides a theoretically rigorous and reliable equivalent and approximate solution for the near-field calculation when a free-form light source illuminates the edge of a polygon deflected at an arbitrary angle. Furthermore, it completely replaces the need for rigorous 3D simulation with a rigorous 2D electromagnetic method, thereby improving the solution efficiency by approximately 1000 times. The edge near-field generated by this method can be reliably and effectively applied to the correction of the 3D near-field of a mask, achieving accurate lithographic imaging calculations.

[0091] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An equivalent method for optical near-field, characterized in that, include: Step 1: Set up a three-axis coordinate system so that the initial propagation direction of the light source at the preset angle propagates along the first axis, and obtain the initial wave vector and polarization direction. Step 2: Rotate the initial wave vector and polarization direction once along the second axial direction and once along the third axial direction according to the preset angle of the light source. Step 3: Analyze the polarization direction and polarization vector of the light source after the rotation operation; Step 4: Rotate the polygon and the light source according to the preset angle of the polygon so that the angle of the polygon becomes 0 degrees and the direction of the light source relative to the edge of the polygon remains unchanged. Step 5: Obtain the new wave vector and the corresponding rotation angle; Step 6: Analyze the polarization direction, polarization vector, and composition of the light source after the second rotation operation based on the rotation angle obtained in Step 5. Step 7: Decompose the polarization vector into its corresponding polarization direction to obtain the components in each polarization direction; Step 8: Generate the edge near field under equivalent conditions using a 2D rigorous electromagnetic algorithm; Step 9: Based on the polarization direction of the light source after the second rotation operation, linearly superimpose the corresponding components to obtain the equivalent near-field results of the light source at the preset angle and the polygon at the preset angle.

2. The equivalent method for optical near-field as described in claim 1, characterized in that, The three-axis coordinate system is the xyz-axis coordinate system.

3. The equivalent method for optical near-field as described in claim 1, characterized in that, When the first axial direction is the x-axis, the second axial direction is the y-axis, and the third axial direction is the z-axis, the polarization direction along the y-axis in step 3 is... The polarization direction along the z-axis is The polarization vector is α and β are preset angles of the light source, p is the initial component along the y-axis polarization direction, and q is the initial component along the z-axis polarization direction.

4. The equivalent method for optical near-field as described in claim 3, characterized in that, In step 6, the polarization direction along the y-axis after the light source undergoes a second rotation is... The polarization direction along the z-axis is The polarization vector is , The preset angle for the polygon. , .

5. The equivalent method for optical near-field as described in claim 4, characterized in that, In step 7, the components of polarization vector P2 along polarization direction Ey2 are: The polarization vector's components along the polarization direction Ez2 are: .

6. A method for correcting the near field of a 3D mask, characterized in that, An equivalent method for the near field as described in any one of claims 1 to 5 is employed.

7. A computer storage medium for storing computer programs, characterized in that, When the computer program is executed, it performs the near-field equivalent method as described in any one of claims 1 to 5.

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